J. Chem. Eng. Data 2008, 53, 211–216
211
Density, Viscosity, Refractive Index, Excess Molar Volume, Viscosity, and Refractive Index Deviations and Their Correlations for the (Formamide + Water) System. Isobaric (Vapor + Liquid) Equilibrium at 2.5 kPa Viviana Campos, Ana C. Gómez Marigliano, and Horacio N. Sólimo* Departamento de Física - Facultad de Ciencias Exactas y Tecnología, Universidad Nacional de Tucumán, Avenida Independencia 1800, 4000 San Miguel de Tucumán, Argentina
Density, viscosity, and refractive index measurements for pure formamide and water at T ) (293.15, 303.15, 313.15, and 323.15) K as well as for the binary system {x1 formamide + (1-x1) water} at the same temperatures were made over the whole concentration range. Isobaric (vapor + liquid) equilibrium at P ) 2.5 kPa for this binary system was also measured. The experimental results of density, viscosity, and refractive index were fitted to empirical equations, which makes it possible to calculate these properties over the whole studied concentration and temperature ranges. Calculated values are in good agreement with the experimental results. Data of the binary mixture were further used to calculate the excess molar volume, viscosity and refractive index deviations, and the activity coefficients. The excess or deviation properties were fitted to the Redlich–Kister polynomial relation to obtain their coefficients and standard deviations. This binary system shows negative deviations from the ideal behavior and no azeotrope.
Introduction Excess thermodynamic functions and deviations of nonthermodynamic ones of binary liquid mixtures are very important for the design of industrial equipment and for the interpretation of the liquid state, particularly when polar components are involved. In this paper, we report density F, viscosity η, and refractive index nD data for pure formamide and water as well as for the binary system constituted by these two chemicals in the whole mole fraction range at T ) (293.15, 303.15, 313.15, and 323.15) K. Isobaric (vapor + liquid) equilibrium (VLE) data are also reported at P ) 2.5 kPa. From these experimental results, excess molar volume V E, viscosity ∆η and refractive index ∆nD deviations from the ideal behavior, and activity coefficients γi were calculated. Empirical equations for the density, viscosity, and refractive index of pure components as a function of the temperature as well as for the binary system as a function of temperature and composition were applied to the measured data. These equations are useful for interpolation within the studied temperature range. The excess and deviation properties were fitted to a Redlich– Kister-type1 equation using least-squares to obtain their dependencies on concentration and temperature. Associations between formamide and water molecules at T ) 298 K have been previously observed using proton magnetic relaxation data.2 Also, the heat of solution, heat capacity, and density of this system at T ) 298.15 K have been reported by Egan et al.,3 while Sköld et al.4 report enthalpies of solution at infinite dilution at T ) 298.15 K. However, as far as we know, neither isobaric VLE data nor excess molar or deviation properties at temperatures other than those stated above are available in the literature for this binary system. This work is a part of an ongoing research program in which we study thermodynamic, transport, and spectroscopic properties * Corresponding author. E-mail:
[email protected].
of binary mixtures containing formamide as one of the components.5–8
Experimental Section Materials. Formamide (analytical reagent) was supplied by Riedel-de Haën. It was used as received because no impurity was detected by gas chromatography using an HP 6890 gas chromatograph with an FID detector, showing that its mole fraction was higher than 0.998. Formamide was stored over 0.3 nm molecular sieves to prevent water absorption, and its water content was periodically checked by Karl Fischer titration using an automatic Mettler DL18 Karl Fischer titrator. Degassed bidistilled water was used. Apparatus and Procedure. For density, viscosity, and refractive index measurements, liquid mixtures were prepared by weighing each component in airtight-stoppered bottles, keeping in mind the vapor pressures of the components when establishing the filling sequence. Each mixture was immediately used after it was well mixed by shaking. All the weightings were performed on a dual-range electronic balance (Mettler Toledo AG-245) accurate to 0.1/0.01 mg. The uncertainty in the mole fractions for these mixtures is estimated to be lower than ( 1 · 10-4. Density, refractive index for the sodium D-line, and viscosity were measured with a vibrating tube densimeter KEM DA-300 with a built-in thermostatic unit accurate to 0.01 K, which allows working over the range T ) (277 to 363) K using degassed bidistilled water and dry air as calibrating substances, a Leica AR600 refractometer, and a Schott-Gerätte AVS 400 viscometer with appropriate Ubbelohde capillary viscometers calibrated by the manufacturer, respectively. The accuracies were of ( 0.1 kg · m-3 for density, ( 0.00005 for refractive index, and ( 0.001 mPa · s for viscosity. A Schott CT 1450 thermostatically controlled water bath, with an uncertainty of ( 0.01 K, was used for viscosity measurements.
10.1021/je700517f CCC: $40.75 2008 American Chemical Society Published on Web 11/27/2007
212 Journal of Chemical & Engineering Data, Vol. 53, No. 1, 2008 Table 1. Density G, Refractive Index nD, and Viscosity η Values at Several Temperatures and Boiling Temperature at 2.5 kPa of the Pure Components F/kg · m-3
a
T/K
exptl
293.15 303.15 313.15 323.15
1133.0 1124.6 1116.1 1108.0
293.15 303.15 313.15 323.15
998.2 995.7 992.2 988.0
η/mPa · s
nD lit.
1133.39a 1124.6b 1116.1b 1107.8c 998.2058a 995.6504a 992.2191a 988.0382a
exptl
lit.
Formamide 1.44802 1.44432 1.44054 1.43705 Water 1.33365 1.33254 1.33055 1.32904
exptl
lit.
1.44754a 1.44432b 1.44054b
3.792 2.941 2.361 1.966
3.764a 2.83a 2.36b 1.92d
1.3329880a 1.3319405a 1.3306096a 1.3290364a
1.011 0.807 0.662 0.556
1.0019a 0.79726a 0.65263a 0.54675a
boiling temperature at 2.5 kPa · K-1 359.5
279.4
From ref 14. b From ref 5. c From ref 6. d From ref 22.
Table 2. Experimental Density G, Viscosity η, and Refractive Index nD for {x1 Formamide + (1-x1) Water} at Several Temperatures F/kg · m-3
η/mPa · s
nD
x1a
T/K ) 293.15
303.15
313.15
323.15
293.15
303.15
313.15
323.15
293.15
303.15
313.15
323.15
0.0000 0.0753 0.1519 0.2309 0.2959 0.3852 0.4854 0.5652 0.6138 0.6924 0.7676 0.8175 0.9254 1.0000
998.2 1024.3 1043.7 1061.5 1072.2 1083.5 1095.2 1103.1 1107.1 1114.5 1119.2 1122.6 1129.1 1133.0
995.7 1019.9 1038.1 1054.5 1065.4 1076.5 1087.6 1095.3 1100.4 1105.8 1110.9 1114.3 1120.6 1124.6
992.2 1014.9 1032.2 1048.4 1058.3 1068.9 1079.8 1087.3 1091.3 1097.1 1102.7 1105.9 1112.2 1116.1
988.0 1009.4 1026.0 1041.7 1051.3 1061.6 1072.2 1079.7 1084.0 1090.3 1094.8 1097.9 1104.1 1108.0
1.33375 1.35293 1.36831 1.38233 1.39192 1.40215 1.41250 1.41967 1.42395 1.42992 1.43511 1.43806 1.44420 1.44805
1.33250 1.35045 1.36573 1.37948 1.38925 1.39904 1.40943 1.41696 1.42167 1.42755 1.43233 1.43482 1.44070 1.44434
1.33062 1.34864 1.36377 1.37773 1.38711 1.39620 1.40688 1.41414 1.41862 1.42415 1.42860 1.43121 1.43676 1.44050
1.32905 1.34732 1.36233 1.37585 1.38480 1.39411 1.40344 1.41038 1.41455 1.42011 1.42482 1.42750 1.43334 1.43715
1.011 1.098 1.195 1.318 1.446 1.603 1.814 2.035 2.162 2.401 2.692 2.930 3.418 3.792
0.807 0.886 0.973 1.073 1.182 1.306 1.473 1.631 1.743 1.932 2.145 2.313 2.661 2.941
0.662 0.734 0.811 0.898 0.988 1.089 1.227 1.353 1.441 1.586 1.757 1.891 2.155 2.361
0.556 0.621 0.688 0.788 0.840 0.924 1.042 1.144 1.220 1.343 1.477 1.574 1.784 1.966
a
Mole fraction of formamide.
Isobaric VLE data were obtained with commercial equipment (Labodest, model 602-S) available from Fischer Technology, Germany. The equilibrium temperatures were measured with a digital temperature logging module tmg (Temperaturmeßtechnik Geraberg GmbH, Germany), type DTM5080 with a Pt-100 temperature sensor, calibrated by the manufacturer with an uncertainty of 0.02 K, whereas total pressure in the still was measured with a precision pressure transmitter (Wika, model P-10) with an uncertainty of 0.01 kPa, both connected to the Fischer VLE2+ vacuum and temperature control unit. Samples of the condensed vapor and liquid phases were taken at stationary conditions, and their equilibrium compositions were determined by gas chromatography. A Hewlett-Packard 6890 gas chromatograph with an automatic injector (Agilent G2613A) directly connected to a ChemStation (HP G2070AA) was used, and the internal standard method was applied to obtain quantitative results. Acetone (Merck, chromatographic quality) with a mole fraction purity >0.998 (GC) was the standard compound used for this purpose. Good separation of all components was obtained on a 30 m long × 0.25 mm inner diameter × 0.5 µm film thickness cross-linked polyethylene glycol capillary column (HP-INNOWax 19091N-233). The temperature program used was as follows: initial temperature T ) 343 K for 2 min, ramp of 50 K · min-1, and final temperature T ) 513 K for another 5 min. The nitrogen carrier gas flow was kept constant electronically, working with a split ratio of 20:1 and with the injector maintained at T ) 503 K. Detection was conducted by a thermal conductivity detector at T ) 523 K. Three analyses were performed for each sample to obtain a mean mole fraction value with repeatability better than 1 %. The analytical balance described above was used in the range accurate to ( 0.01 mg both for the calibration curves and for
the analysis of the unknown samples, and 10 mixtures were prepared to obtain the calibration curves for each component. To validate the reported mole fraction values, three samples of well-known compositions (determined by mass) were analyzed. These analyses show that the reported mole fraction values have an uncertainty of ( 0.001.
Results and Discussion Experimental results for refractive index, density, and viscosity of pure compounds at several temperatures are summarized in Table 1. For comparison, existing values found in the literature are also included. Experimental results for the density, viscosity, and refractive index corresponding to temperatures over the range T ) (293.15 to 323.15) K for the system {x1 formamide + (1-x1) water} are listed in Table 2. To obtain empirical correlations for pure compounds with temperature, the following functional relationships for density, refractive index, and viscosity were used:
F ⁄ kg · m-3 ) a1 + b1 · (T ⁄ K)
(1)
nD ) a2 + b2 · (T ⁄ K)
(2)
η ⁄ mPa · s ) a3 · exp[b3 ⁄ (T ⁄ K)]
(3)
where ai and bi are constants given in Table 3 together with the standard deviations. These equations were fitted using leastsquares with all points equally weighted, which allows evaluation of all constants. The appropriate number of significant digits was selected taking into account the above-reported experimental errors for density, viscosity, refractive index, and temperature. Calculated values from these equations compare
Journal of Chemical & Engineering Data, Vol. 53, No. 1, 2008 213 Table 3. Coefficients and Standard Deviations of Equations 1, 2, and 3 F/kg · m-3 compound
a1
b1
η/mPa · s
nD σ
4
4
3
10 b2 10 σ 10 a3
a2
formamide 1377.6 -0.835 0.1 1.5555 -3.67 water 1098.6 -0.341 0.6 1.3802 -1.58
1 3
2.8 1.5
σ
b3
2111 0.04 1907 0.006
well with experimental data within the standard deviations reported in Table 3. Polynomial equations were used to correlate the same properties for {x1 formamide + (1-x1) water}, as follows
F ⁄ kg · m-3(x1, (T ⁄ K)) )
m
n
∑ ∑ aij · (T ⁄ K)i · x1j
(4)
i)0 j)0
m
nD(x1, (T ⁄ K)) )
n
∑ ∑ bij(T ⁄ K)i · x1j
(5)
i)0 j)0
m
η ⁄ mPa · s(x1, (T ⁄ K)) )
∑ cj · x1j · exp[dj · x1j ⁄ (T ⁄ K)]
(6)
j)0
where aij, bij, cj, and dj are parameters given in Table 4 together with their standard deviations. Equations 4, 5, and 6 were fitted using a nonlinear regression method based on the Levenberg–Marquardt algorithm.9 These fits show linear behaviors for density and refractive index with temperature, while for viscosity, this dependence is exponential. To obtain the respective dependencies on composition and temperature, we adopt the same procedure that was previously described.5,6,8,10 The appropriate number of significant digits was selected taking into account the experimental errors for density, refractive index, viscosity, and temperature reported above. Equations 4, 5, and 6 make it possible to predict the density, refractive index, and viscosity of the binary system at any concentration and over the temperature range T ) (293.15 to 323.15) K, respectively, using the parameters reported in Table 4 within its respective standard deviation σ. Values calculated with these equations compare well with experimental data, and the standard deviations are similar to those obtained in previous works.5,6,10 On the other hand, the excess molar volume VE, viscosity deviation ∆η, and refractive index deviation ∆nD, were calculated using the following equations:
V E ⁄ m3 · mol-1 ) [(x1 · M1 + (1 - x1) · M2) ⁄ F] M1 M2 x1 + x2 (7) F1 F2
(
)
∆η ⁄ mPa · s ) η - [x1 · η1 + (1 - x1) · η2]
(8)
∆nD ) nD - (φ1 · nD1 + φ2 · nD2)
(9)
log(Pio ⁄ Pa) ) Ai - Bi ⁄ [(T ⁄ º C) + Ci]
(11)
Fitting our experimental vapor pressure values for formamide, listed in Table 5, and using least-squares with all points equally weighted, the Antoine constants Ai, Bi, and Ci were calculated using eq 11. The values so obtained are also reported in Table 5. The significant digits of each constant were established taking into account their standard deviations. Using these constants, the vapor pressure of formamide can be calculated with a standard deviation of 0.08 kPa. The VLE data reported in Table 6 for {x1 formamide + (1-x1) water} were plotted in Figure 1, which shows that this binary system presents negative deviations from the ideal behavior and no azeotrope. These VLE data were found to be thermodynamically consistent according to the point-to-point test of Van Ness et al.,12 as modified by Fredenslund et al.13 Consistency criteria were met using a one-parameter Legendre polynomial. The average absolute deviations in vapor-phase mole fractions and pressure are ∆y ) 0.02 and ∆P ) 0.60 Pa, respectively. The excess molar volume and viscosity and refractive index deviations were fitted to the experimental results by means of a Redlich–Kister-type equation1 with the same fitting procedure as indicated above: n
Y E ) x1(1 - x1)
∑ ej(1 - 2x1)j
(12)
j)0
where Y E represents either V E, ∆η, or ∆nD. Since the coefficients ej are functions of the temperature, they were plotted against this variable to obtain equations that represent each property over the studied temperature range. We propose the following dependence with temperature for these coefficients, as previously6,8,10 m
ej )
∑ eji · (T ⁄ K)i
(13)
i)0
where x1 is the mole fraction of formamide; M1 and M2 are the molar masses of formamide and water, respectively; F, nD, and η are the density, refractive index, and viscosity of the mixture; F1, F2, nD1, nD2, η1, and η2 are the densities, refractive indices, and viscosities of the pure components; and φ1 and φ2 are the mole volume fractions of the pure components. The activity coefficients of formamide γ1 and water γ2, in the liquid phase, are related to VLE by
γi ) yiP ⁄ xiPio
pressure and the pure component vapor pressure, respectively. In eq 10, the vapor phase is assumed to be an ideal gas, and the pressure dependence of the liquid-phase fugacity is neglected. This equation was selected to calculate activity coefficients because the work pressure is low, which makes this simplification reasonable. Vapor pressures of pure formamide over the range P ) (0.280 to 26.700) kPa were determined experimentally as a function of temperature, using the same equipment as for the VLE measurements. The pertinent results appear in Table 5 together with literature values reported by Stull.11 As can be seen, our values do not agree with those of Stull, which are always significantly lower. On the other hand, vapor pressures of pure water were calculated over the whole range of temperatures listed in Table 6 applying the Antoine equation, with the constants reported in the literature:14
(10)
where xi and yi are the equilibrium mole fractions in the liquid and vapor phases of component i, and P and Pio are the total
Using this temperature dependence, eq 12 can be rewritten as follows n
Y E ) x1(1 - x1)
m
∑ ∑ eji · (T ⁄ K)i · (1 - 2x1)j
(14)
j)0 i)0
where the eji parameters are also given in Table 4 together with their standard deviations σ, defined as
σ)
[∑ (Y
1⁄2 E E 2 exptl - Ycalcd ⁄ (N - p)
)
]
(15)
where N and p are the numbers of experimental points and parameters, respectively. The choice of the appropriate number
214 Journal of Chemical & Engineering Data, Vol. 53, No. 1, 2008 Table 4. Coefficients and Standard Deviations of Equations 4, 5, 6, and 14 property
i-j
aij
property
F/kg · m-3(x1, T/K)
σ η/mPa · s(x1, T/K) j 0 1 2 σ
0–0 0–1 0–2 0–3 1–0 1–1 1–2 1–3 1/kg · m-3
1106.0 833 -1016 459.3 -0.3608 -1.72 2.31 -1.08
cj 0.0015 0.011 0.01
dj 1857.9 -695 1000 0.06/mPa · s
σ
bij
σ ∆nD(x1, T/K) j-i 0–0 0–1 0–2 1–0 1–1 1–2 0.02/mPa · s
σ
eji -125 0.759 -1.16 · 10-3 45.2 -0.28 4.37 · 10-4
σ Table 5. Experimental and Literature Vapor Pressure Data for Formamide at Several Temperatures and Antoine Coefficients for Equation 11 P/Pa
P/Pa
T/K
exptl
lit.a
T/K
exptl
lit.a
348.4 359.3 371.7 386.3
280 650 1300 2670
182 359 741 1638
401.8 411.9 425.3 444.5
5330 8000 13330 26700
3569 5744 10430 23028
antoine equationb
Ai
Bi
Ci
formamide
8.24669
1098.42418
114.96308
Interpolated from ref 11. b Eq 11.
Table 6. Experimental Results for the Mole Fraction of Formamide in the Liquid x1 and Vapor y1 Equilibrium Phases, Temperature T, and Calculated Activity Coefficients γi for {x1 Formamide + (1-x1) Water} at P ) 2.5 kPa x1
y1
T/K
0.000 0.232 0.391 0.466 0.545 0.589 0.748 0.806 0.879 0.937 1.000
0.000 0.004 0.004 0.005 0.002 0.002 0.004 0.025 0.076 0.364 1.000
279.4 293.55 302.05 305.97 310.05 314.82 320.45 330.75 339.05 352.75 359.5
0–0 0–1 0–2 1–0 1–1 1–2 0.007
1.39766 0.2820 -0.127 -1.59157 · 10-4 -4.4528 · 10-4 2.5008 · 10-4
j-i 0–0 0–1 0–2 1–0 1–1 1–2 2–0 2–1 2–2 9 · 109/m3 · mol-1
eji -1.575 · 10-5 8.96 · 10-8 -1.297 · 10-10 1.075 · 10-5 -8.02 · 10-8 1.416 · 10-10 -1.467 · 10-5 8.74 · 10-8 -1.322 · 10-10
j-i 0–0 0–1 0–2 1–0 1–1 1–2 2–0 2–1 2–2 3 · 10-3
eji 0.42 -2.5 · 10-3 3.9 · 10-6 0.4 -2.4 · 10-3 3.7 · 10-6 0.26 -1.7 · 10-3 2.7 · 10-6
VE/m3 · mol-1(x1, T/K)
∆η/mPa · s(x1, T/K)
a
i-j
nD(x1, T/K)
γ1 31.93 6.280 4.131 0.892 0.497 0.447 1.022 1.453 2.438 4.058
of formamide for the binary system at several temperatures, respectively. These plots show that the excess molar volumes and viscosity deviations are always negative, while the refractive index deviations are always positive over the whole studied concentration and temperature ranges. Furthermore, and for any composition, when temperature is increased, the excess molar volume and viscosity deviation values become less negative while refractive index deviation values become less positive. Usually, the excess molar volume and the viscosity deviation have opposite signs. However, for {x1 formamide + (1-x1) water}, this does not happen, as can be seen in Figures 2 and 3. This behavior is also observed for other binary systems.15–18 As can be seen in Figure 3, the viscosity deviations are negative for all the studied temperatures and over the whole composition range, which would correspond to binary systems
γ2 2.628 1.353 1.027 0.935 0.878 0.753 0.917 0.705 0.733 0.541
of constants in eq 14 was based on the variation with n and m of the standard error of the estimated value. The significant digits of each coefficient were established taking into account their standard deviation. Figures 2, 3, and 4 show the excess molar volumes, viscosity, and refractive index deviations, plotted against the mole fraction
Figure 1. Plot of temperature T/K against 9, liquid-phase mole fractions x1; and O, vapor-phase mole fractions y1 for {x1 formamide + (1-x1) water} at P ) 2.5 kPa. Error bars have the same size of the symbols.
Journal of Chemical & Engineering Data, Vol. 53, No. 1, 2008 215
index deviation from ideal behavior. For many binary systems, in which spectroscopic or other methods indicate that molecular interactions occur, ∆nD was found to be greater than 0.004. Therefore, these authors conclude that ∆nD > 0.004 is an indication of complex formation. Although several types of intermolecular complexes between formamide and water in the solution were previously reported by Sukhno et al.,2 the ∆nD values for {x1 formamide + (1-x1) water} are always lower than 0.004 (see Figure 4), probably due to the high selfassociation of formamide and water.
Literature Cited Figure 2. Plot of excess molar volume VE against mole fraction x1 for {x1 formamide + (1-x1) water}: T ) 9, 293.15 K; b, 303.15 K; 2, 313.15 K; 1, 323.15 K. Solid lines correspond to the least-squares fit using eq 14. ψ, error bars.
Figure 3. Plot of viscosity deviation ∆η against mole fraction x1 for {x1 formamide + (1-x1) water}: T ) 9, 293.15 K; b, 303.15 K; 2, 313.15 K; 1, 323.15 K. Solid lines correspond to the least-squares fit using eq 14. ψ, error bars.
Figure 4. Plot of refractive index deviation ∆nD against mole volume fraction φ1 for {x1 formamide + (1-x1) water}: T ) 9, 293.15 K; b, 303.15 K; 2, 313.15 K; 1, 323.15 K. Solid lines correspond to the least-squares fit using eq 14. ψ, error bars.
that exhibit negative deviations from Raoult’s law. The sign of ∆η is also in agreement with the conclusion reported by Fort and Moore19 and with the endothermic behavior of this binary system.3 As can be observed in Figure 3, increasing the temperature leads to less negative ∆η values, due to an increase of the thermal energy. Intermolecular complexes have also been investigated by Voronkov et al.20,21 using methods based upon the refractive
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Received for review September 7, 2007. Accepted October 11, 2007. The authors are indebted to the Agencia Nacional de Promoción Científica y Tecnológica (Grant: PICTO 2004 n° 633) of Argentina for financial support.
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